worth doing a bit of model-specific research online (owners forums or similar) for any issues related specifically to 3rd gear on that model.
A problem with the gearbox is sort of pretty likely to be ‘the gearbox’ but it could be clutch related – the clutch isnt releasing properly to allow the gear change – or it could be an issue with the gear selector – something stiff/slack/worn/loose between the gear stick and the gearbox that means the gear isnt being selected properly. The route from the gear stick to the gearbox can sometimes be pretty indirect so there can be linkages and cables going round bends and any of them being stiff, worn, dirty could be the issue
So a first step might be to get a garage to check everything external to the gearbox is adjusted and lubricated properly and nothing is worn. If thats ruled out then it’s probably an exchange / refurbished gearbox. Often a local garage won’t do this themselves and they’ll take it to a local specialist, so if you don’t get on with your local garage maybe look up local gearbox specialists and deal with them direct – they usually replace them on an exchange basis, taking your old gearbox as effective part payment for reconditioned on. A recon box will usually cost about £300-400 plus labour. It’s the sort of thing where you’re as well getting the clutch done too while it’s accessible.