She spends most of her free time playing the piano.

Literal

She [topic-は] free time [when-時は], mostly piano [object-を] is-playing.

暇な時 = 'when (she) has free time,' a noun-modifying clause with な (from the na-adjective 暇 'free, idle') sitting before 時. The sentence-internal は after 時 is the topical-contrastive は, marking the time-frame as the topic for the predicate that follows. ピアノを弾く = 'play the piano' uses 弾く ('strum, pluck') — the verb for string and keyboard instruments, distinct from 吹く (winds) or 叩く (drums). The ~ている form here describes a habitual action, not a single moment of playing.