Leader’s position in group’s last run of gigs (10)

I believe the answer is:

presidency

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'leader's position' is the definition.
'presidency' can be an answer for 'position' (presidency is a kind of position). I am unsure of the 'leader's' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for presidency that I've seen before include "Top position" , "place at the top" , "Office at the top" , "US office" , "Monroe once took on" .)

I've seen this clue in The Times.

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