Old rubbish men spotted in the course of walk or fun run (6,4)

'fun run' is the definition.
(type of humorous race)

'old rubbish men spotted in the course of walk' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'rubbish' becomes 'tat' (low-quality items or material).
'men' becomes 'or' (military abbreviation for Other Ranks).
'spotted in' indicates putting letters inside.
'the course of walk' becomes 'pace' (the speed of a walk).
'o'+'tat'+'or'='otator'
'otator' put into 'pace' is 'POTATO RACE'.

'or' acts as a link.