I'm looking for Edges/Hindrances to allow a player to play a character who focuses on defending other characters. We don't use miniature combat a lot (thus far they've been fairly small), and I don't have a lot of familiarity with powers and Edges from other SW settings.
There's a number of ways to build a defensive fighter. I'm going to assume you're not using powers/magic (though there are a lot of good defensive powers too).
There's some non-edge stuff to consider first, like attributes:
After setting up your attributes, it's time to start picking edges. I would not recommend most leadership edges, as they mostly only apply to NPCs. If you're limited to core rules, you might ask your GM to house-rule leadership edges to work on PCs.
I've listed a few edges that I think are useful for defensive fighters. Many of these edges have improved versions that aren't listed. This is in no way a conclusive list:
Finally, there's one last ability that's worth mentioning. Absorption from Necessary Evil allows you to absorb attacks against you and increase your Vigor instead of taking damage. If you're allowed to combine settings, the Guardian edge and Absorption power make for a ridiculous combination.
Guardian, from Slipstream, is the big one. This allows you to take any hits directed at the person you are protecting as long as you stay close to them.
It's probably way too good actually. If you're not using minis, just say your character is next to the person you're defending.
There are a number of approaches that come to mind, but the big caveat with all of them is that it depends on the setting you are working in and what you're GM does and doesn't allow. It is very important to note that Edges from different settings are not intended to be 'plug and play', and they are not guaranteed to be balanced if you start mixing and matching from different settings. As you've not specified this, I'll try to keep my answer as generic as possible.
There are no Edges in the core rules that actively allow you to increase the melee defense of your allies. However, in a couple of the settings there are Edges that allow your allies to take the Parry increase from your shield if you are adjacent to them. There are also a couple that allow you to negate some of your enemies Ganging Up bonuses by standing adjacent.
A big part of your role will be being in the right place at the right time. One approach to this could be mainly staying on Hold and interrupting your opponents once the target of their attacks is clear. This will require high Agility, as successful interruption requires an opposed Agility roll. If you employ this tactic at range then Edges such as Marksman are good (although only available at Seasoned rank), as they give you bonuses to hit as long as you don't move.
Tactical manoeuvreability could also be important, so Edges like Fleet Footed, Extraction and Improved Extraction might be helpful. It would also be useful to guarantee high initiative cards, so Quick and Level Headed (Seasoned only) could both be useful.
By positioning yourself correctly, you can use the First Strike Edge to get one free attack each turn against foes that move adjacent to you. At Heroic rank, Improved First Strike can also be purchased that gives you this attack against all foes that move adjacent.
To make your allies more difficult to hit with ranged attacks, the obvious thing to do is to increase their cover by putting yourself between them and the aggressor. This is usually equivalent to giving them a +1 cover bonus as medium cover.
Common Bond allows you to give your Bennies to allies to help Soak damage and remove Shaken statuses. If you go down this route then Luck and Great Luck are good as they give you extra bennies to play with.
The various Leadership Edges give passive bonuses to subordinate allies within your command radius (typically 5"). e.g. Command improves their chances of recovering from being Shaken, whilst Hold the Line! gives them +1 Toughness. However, you should check with your GM as to what they interpret subordinate to mean. Although the Deluxe version of the rules have softened this requirement considerably, different genres/settings might still require the allies benefiting to roleplay their subordinate position.
Lastly, there is the possibility of acting as an 'early warning system'. High Notice becomes desirable here as do the Alertness and Danger Sense Edges. If you want to protect your allies then nothing beats spotting dangers/ambushes early.
As you have specified that you are playing a fighter, I haven't gone too much into powers. However, should you have access to Arcane Backgrounds and they fit with your character concept then there are numerous Powers you can cast to help your allies, including Deflection, Barrier and Armour.