Possible Clues:

• Covered walk by cathedral etc
• Cathedral's covered walk
• Covered walkway in religious institution
• Costlier (anag) – secluded setting
• Covered walk in religious institution
• Lane, in films, flanked by court, a royal and religious place
• Place of religious seclusion, a convent say
• Monastic life is embraced by dimwit with hesitation
• Damage to relics in ambulatory
• College head to hang around school corridor?