、。
She loved tennis, so she became a tennis coach.
Literal
She [topic-は] tennis [subject-が] liked [because-で], tennis [genitive-の] coach [to-に] became.
The te-form 好きで links cause and effect: 'because (she) likes tennis, (she) became a coach.' で here is the te-form of the copula だ — the same で that connects multiple predicates ('A is X and Y') doubles as a soft 'because' when the link is causal. The frame [noun]＋に＋なる ('become X') is one of the foundational change-of-state patterns in Japanese; it pairs with [い-adj]＋く＋なる for adjective-stem changes (寒くなる 'become cold'). コーチ is a loanword from English, settled in Japanese sports vocabulary.