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She makes sure to keep up with the latest trends.
Literal
She [topic-は] recent [genitive-の] trend [from-に] not-fall-behind [so-as-to-ように] is-doing.
The frame ~に遅れないようにする ('make sure not to fall behind X') stitches together a negative verb (遅れない 'not fall behind') + ように ('so as to') + する ('do') to express an effortful, ongoing habit aimed at avoiding a state. The progressive ~している locates this as her present, ongoing practice rather than a one-off effort. Pair the whole construction with 流行 ('trend, what's catching on') and you get the canonical Japanese phrasing for fashion-conscious effort: not 'follows trends' but 'works at not falling behind them.' The negative-frame phrasing matches a Japanese cultural attentiveness to keeping pace with the group rather than standing out ahead of it.