。
If you praise her, she'll get full of herself.
Literal
Praise-[if-と] she [topic-は] become-conceited [emphasis-よ]
The ~と conditional ('whenever X happens, Y') is used here for a habitual/generic consequence — 'every time you praise her, the result is Y'. うぬぼれる ('to be conceited, to be full of oneself') is a slightly humorous or critical verb about self-regard.