If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends. A member of a group can be surprised even if the other members aren't.
This particular wording leads me to believe that if an enemy's first turn occurs after initial start of a combat encounter (ie. reinforcements), they could still suffer the Surprised condition as stated above from a single player if they aren't high enough in the initiative. Also, if one member can be surprised while others are not, could the same not be said of the character(s) initiating the surprise?
Story behind question below:
I was in a game where we were fighting a Hook Horror. Playing an Assassin Rogue, I was in Stealth and the passive perception (or active, for that matter) of the Hook Horror* couldn't meet my Stealth (Move Silently) check. As a result, I gained a single round before the rest of the party arrived to initiate combat with the Hook Horror in the Surprised condition. It called out, echoing through the tunnels and summoned more which were to arrive in a few turns. We dispatched it before reinforcements arrived, during which I rolled another Stealth (Move Silently). The next round came up and the reinforcements arrived. I was at the top of the initiative and got to go first and asked the DM if the new Hook Horror would be considered surprised as well, since it still couldn't beat my Move Silently stealth. Mulling it over for a few seconds, she decided that it would, in fact, be surprised as it had not yet been part of combat.
Obviously, this has already happened and won't change that it did, but for future reference, I'd like the input of some fellow rule nerds about how this should play out. The rules state that a Surprised creature cannot act on its first turn of the combat encounter, so the argument in question is, if a creature enters combat later than the original first round, can it still be surprised by one or more players who have opted for stealth?
*I know Hook Horrors have hearing-based blindsight and advantage on hearing-based Wis(Perception), but my stealth was a specifically a move silently check as we were in the Underdark and my character was a Drow with (rolled for) knowledge of such things, as well as other species/races having darkvision that would nullify a traditional Hide check.