Every seven days, leader apparently turned up submissively (6)
I believe the answer is:
meekly
'submissively' is the definition.
(I've seen this before)
I cannot understand how the rest of the clue works.
(Other definitions for meekly that I've seen before include "In submissive or passive manner" , "In a mild and submissive manner" , "In gentle, acquiescent manner" , "Humbly" , "In a submissive way" .)