Ex-PM picked up female on the game (5)
I believe the answer is:
nehru
'ex-pm picked' is the definition.
I can't tell whether this defines the answer.
'up female on the game' is the wordplay.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'female' becomes 'hen' (female chicken).
'on' is a charade indicator (letters next to each other).
'the game' becomes 'RU' (rugby union).
'hen' in reverse letter order is 'neh'.
'neh'+'ru'='NEHRU'
Can you help me to learn more?
(Other definitions for nehru that I've seen before include "Old statesman" , "former statesman" , "Famous Indian" , "First Indian PM" , "First prime minister of India" .)