Promoting the pawn will win easily for White. With King and Queen against King, the proces of forcing mate is elementary.
Can the Pawn advance at once, or will it be caught by Black? Let’s try moving the Pawn and see:
- h4 Kc4
- h5 Kd5
- h6 Ke6
- h7 Kf7 5.
- h8=Q
White wins.
We can thus play out the moves (mentally, of course) or get the answer by a simple count. The latter method tells us that after four moves the Pawn will stand at h7, and Black’s pursuing King at f7 - too late to stop the Pawn from Queening.