We may distinguish two essentially different cases:
a ) the black king is far from the pawn,
b ) the black king is in front of the pawn.
When the black king is far from the pawn, whilst the white king supports the pawn and controls one of the critical squares on its way to promotion, the situation is trivial. The goal will be easily accomplished by advancing the pawn and preventing the enemy king from controlling the critical squares on the passed pawn’s path to promotion.