Minor problem getting horse into river (6)
I believe the answer is:
niggle
'minor problem' is the definition.
(a niggle is a small problem or complaint)
'horse into river' is the wordplay.
'horse' becomes 'gg' (geegee or GG is a childish term for a horse).
'into' means one lot of letters goes inside another.
'river' becomes 'nile' (Nile is an example).
'gg' put into 'nile' is 'NIGGLE'.
'getting' is the link.
(Other definitions for niggle that I've seen before include "Petty annoyance" , "Persistently criticise over trifles" , "'Small, gnawing worry (6)'" , "Objection" , "Minor criticism - slight worry" .)