Beam, having managed to get in the majority on the way up (7)
I believe the answer is:
transom
'beam' is the definition.
(I've seen this before)
'managed to get in the majority on the way up' is the wordplay.
'managed' becomes 'ran' (I've seen this before).
'to get in' indicates putting letters inside.
'the majority' becomes 'most' (I've seen this before).
'on the way up' shows that the letters should be reversed in order.
'most' back-to-front is 'tsom'.
'ran' inserted into 'tsom' is 'TRANSOM'.
'having' is the link.
(Other definitions for transom that I've seen before include "Horizontal bar across window" , "Crossbar over door" , "Crossbar over a window" , "Cross-member of boat or window" , "Bar above window or door" .)