By outspeed are you asking: if a Pokémon used Protect, is there a move that if you used it on the same turn as the target used Protect you would go first?
Well attacking moves... no... however there is Helping Hand, Helping Hand should only be used in Double or Triple Battles but has +5 Priority.
Detect, Magic Coat, Spiky Shield and Snatch have the same Priority as Protect at +4.
If you're asking whether or not there's a move that has more Priority than Protect but not on the same turn Protect is used then yes there is... Pursuit, however there is a catch:
>If the target opponent switches the Priority of Pursuit is +7, otherwise it is 0.
>If the target Pokémon is switched out on the turn Pursuit is used, Pursuit's power becomes 80 and will deal damage before the Pokémon is switched out.
Despite there being no attacking moves that can outspeed and go first if the target uses Protect, there are moves that Protect cannot stop and will hit a Pokémon even if they have used Protect, these include: