Can you activate a creature's ability that requires tapping it during the declare attackers step after it has already attacked?

A creature that attacks becomes tapped as part of the attack declaration (unless it has Vigilance). Since tapping is a cost for many activated abilities (written as {T} in the cost), and a card that is already tapped cannot be tapped again to pay that cost, you cannot activate a tap-requiring ability with a creature that has already attacked and is now tapped.

This is grounded in CR 602.5a, which states that to activate an ability, you must be able to pay all costs. CR 602.5a combined with CR 117.3 confirms that a cost requiring you to tap a permanent cannot be paid if that permanent is already tapped. CR 508.1f specifies that attacking creatures without Vigilance become tapped during the Declare Attackers step.

There is one important exception: if the creature has Vigilance (CR 702.20), it does not tap when it attacks. In that case, it remains untapped after being declared as an attacker, and you could activate its tap ability later in the combat phase — provided timing and other conditions are met.

Example: You control a Prodigal Pyromancer (tap: deal 1 damage to any target). You declare it as an attacker. It taps to attack. During the Declare Attackers step or later in combat, you cannot activate its tap ability because it is already tapped and you cannot pay the {T} cost again.