I think this one depends a lot on where you are traveling. For some countries, customs/shipping can either be expensive (e.g. DHL) or navigating the import duties/customs route can be troublesome.
So it depends a bit, but I've used all of the following approaches:
1. I've carried more gear than I needed. For example, I carried a lot of cold weather gear through Central America even though it really wasn't needed.
2. I've essentially used a courier, namely someone who was joining later or for a short duration that brought some key pieces.
3. I've bought a few things along the way. For example, I bought an extra sleeping bag to double up in western China - and also got one from a different traveler before ascending to Bolivia Altiplano. I've also shopped in larger places like Lima but not bought anything.
4. I've investigated shipping services for expats. Decided not to use them in that particular case. Again, the key issue is finding someone knowledgeable of how to get goods into particular countries in a timely and cost-effective way
5. I've broken up my trip with a short trip home to pick up additional gear and then flying back in.
Exactly what works for you will likely be situation dependent and hence in addition to posting to this group, I'd suggest browsing additional travel blogs from cyclists going through those areas - since inevitably, something breaks or needs replacing and then that has to be problem solved...