Against a rook pawn, once the defending king reaches the (h8) or stays in front of the pawn, it is a draw: the white king cannot drive it out without it. Head for f8, g8 and h8 and stay there.
Moves
No moves yet.
About this endgame
The rook pawn, the one on the a- or h-file, is the big exception in king and pawn endings. With any other pawn, a well-placed attacking king often wins; with this one, the defender is saved once their king reaches the queening corner. The reason is lack of room. The attacking king cannot go round the defender on the outside, because there is no board out there, and if it tries to drive the defender out of the corner it them. There is another draw worth knowing. If the attacking king walks into the corner, in front of its own pawn, the defender can trap it there: with the pawn on the h-file, the defending king on f7 shuts the way out along the g-file and the game is a draw. Facing a rook pawn, do not think about winning it: think about reaching the corner.