Expedition experiences odd bits of trek (5)
I believe the answer is:
haste
'expedition' is the definition.
(expedition is expediting, doing something quickly)
'experiences odd bits of trek' is the wordplay.
'experiences' becomes 'has' (have can mean to experience or go through).
'odd bits of' means one should take alternating letters.
The alternate letters of 'trek' are 'te'.
'has'+'te'='HASTE'
(Other definitions for haste that I've seen before include "Expedition" , "Promptitude" , "Undue speed" , "Leader abandons modest" , "''Marry in . . . . ., repent at leisure''" .)