Are there any items that give you an extra attack?
The Scimitar of speed seems like exactly what you're looking for.
The scimitar of speed from the Dungeon Master's Guide and the Basic Rules grants you an extra attack":
you can make one attack with it as a bonus action on each of your turns.
The wording of this magic item does not require that you take the attack action or attack with the weapon on your turn, it simply grants you a bonus action attack with the weapon.
A potion of speed, or any magic item that allows you to cast Haste
The text of the Haste spell reads
...and it gains an additional action on each of its turns. That action can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.
So a magic item granting a Haste effect will grant you an extra attack so long as the spell stays in effect.
Another magic item that can grant the Haste spell is the artifact Blackrazor:
Blackrazor can cast the Haste spell on you once per day. It decides when to cast the spell and maintains concentration on it so that you don't have to.
Since you don't have to concentrate on the spell yourself, the potential downsides are limited as you don't risk breaking concentration, Blackrazor does however add the downside of potentially devouring your soul.
The Illusionist's Bracers can give you extra castings of attack cantrips
The Illusionist's Bracers from Guildmaster's Guide to Ravnica reads as follows:
...whenever you cast a cantrip, you can use a bonus action on the same turn to cast that cantrip a second time.
Using this, you could be granted an extra attack of a cantrip such as Booming Blade, Green Flame Blade, or any cantrip that requires an attack roll.
Beyond this, there aren't many magic items that grant extra attacks.
The Scimitar of Speed lets you make an extra attack with it as a bonus action.
The potion of speed grants you the effects of a haste spell, including the ability to take an extra Attack action each turn. (Likewise, any other item that could haste you, like a ring of spell storing, would do the trick.)
Illusionist's Bracers and the Double-Bladed Scimitar, from Guildmaster's Guide to Ravnica and Eberron: Rising from the Last War, respectively, can also increment your ability to make attacks. Those books are outside the "core", though, so there's no assuming a GM is necessarily aware of them, never mind that they'd allow them.
Scimitar of speed
This weapon allows you to make an extra attack with it as a bonus action.