Octane: if you double tap revive, he stims the downed player, getting them up instantly for 20 or so seconds (after which they go back down, further reducing their bleed out time, or if they pop a medkit or something they stay up.)This has a cool down of about 1min.
Bangalore has her smoke
Wraith has her portal
Loba has the ability to throw her bracelet just prior to reviving, causing both reviver and downed player to teleport mid revive to another location (suggested by u/newmann19 )
Gibraltar has his quick revive under the dome
Lifetime has her auto revive drone
Crypto could revive a player through his drone but takes longer
Pathfinder could grapple downed players towards him
Watson could give extra shield back upon revive (or give a burst of speed)
Revenant can revive whilst in shadow form
Caustic has his gas
Mirage has his invisibility
Bloodhound can have a swarm of crows embody them while they revive, acting as a 360 shield (50-100 damage) that can give them an extra second or so to get a revive off. This comes at the cost of being easier to spot.
Rampart could give 10 seconds of extra damage post revive
Edit: whilst I don’t think every legend should have one, it’s fun to think about what would be the ability they would get.