Captain or colonel competed last week (4)

I believe the answer is:
rank
'captain or colonel' is the definition.
I can't tell whether this definition defines the answer.
'competed last week' is the wordplay.
'competed' becomes 'ran' (running is a kind of competing).
'last' suggests the final letters.
The last letter of 'week' is 'k'.
'ran'+'k'='RANK'
Can you help me to learn more?
(Other definitions for rank that I've seen before include "Row of people standing abreast" , "fare might be found here" , "Tier; social standing" , "Stinking" , "Row; foul" .)