The poor old father was granted an audience with the king.
Literal
Poor old-father [subject-が] king [by-に] audience [object-を] was-permitted.
拝見を許された uses 拝見 (humble 'viewing/meeting') with the passive of 許す ('to permit'), creating a respectful expression for being granted an audience. The passive here is honorific, elevating the king's action. 老父 is a formal/literary word for 'old father.'