Reached peak, got rid of unnecessary baggage, beginning ascent (5)
I believe the answer is:
climb
'beginning ascent' is the definition.
'climb' can be an answer for 'ascent' ('climb' can be a synonym of 'ascent'). I am not certain of the 'beginning' bit.
'reached peak got rid of unnecessary baggage' is the wordplay.
'reached peak' becomes 'climaxed'.
'got rid of' becomes 'axed'.
'unnecessary' is a deletion indicator.
'baggage' becomes 'b' (this might be a standard abbreviation I've not previously seen).
'climaxed' with 'axed' taken out is 'clim'.
'clim'+'b'='CLIMB'
(Other definitions for climb that I've seen before include "showing the way up" , "improve one's social status" , "What mountaineer does" , "Slope upwards" , "Go higher up" .)