Every morning, I can hear her singing voice.

Literal

Every-morning her singing-voice [subject-が] is-audible [toward speaker-てくる].

聞こえてくる combines 聞こえる ('to be audible,' involuntary hearing) with ~てくる ('coming toward the speaker') — the sound reaches the speaker. 歌声 ('singing voice') is 歌 ('song') + 声 ('voice'). The subject who hears is omitted.