Can you activate a creature's tap ability during combat after it has been declared as an attacker?

When a creature is declared as an attacker, it is tapped as a cost of attacking (unless it has Vigilance). This happens during the declare attackers step (CR 508.1f). Once a creature is tapped, you cannot pay the tap cost ({T}) of an ability because the creature is already tapped — you can only tap a creature that is untapped (CR 602.5a).

However, if the creature already had a tap ability you wanted to use, you could activate it before declaring it as an attacker — for example, during your main phase before combat, or even during a previous turn. You cannot activate a {T} ability of a creature that is already tapped.

There is an important exception: if the attacking creature has Vigilance (CR 702.20), it does not tap when it attacks. In that case, it remains untapped and you can activate its tap ability later in combat, such as during the combat damage step.

Concrete example: You attack with a Prodigal Pyromancer (tap: deal 1 damage to any target). Once it is declared as an attacker and taps, you cannot activate its tap ability for the rest of combat. If it had Vigilance and stayed untapped, you could activate it during the combat damage step or at end of combat.

The key rules at play are CR 508.1f (creatures tap when declared as attackers), CR 602.5a (you cannot activate a {T} ability of a tapped permanent), and CR 702.20 (Vigilance prevents tapping on attack).