We often enjoy listening to music after dinner.

Literal

Dinner-after music [object-を] listen-[and-て] enjoy-[nominal-こと] [subject-が] often exist-[polite-ます].

A classic habitual construction: [verb]ことがある literally means 'there exist occasions when one does X.' With よく ('often'), it expresses a regular habit. The nominalizer こと turns 楽しむ into an abstract 'the thing of enjoying,' and がある makes it an existential statement — a more detached framing than simple present tense. Used for habits and general tendencies.