Factoring this problem a little, I see two elements that basically multiply together to answer your question:
A. Going forwards, what is the likelihood of new pandemics arising?
1. IMO, the animals/farming angle, and the "people travel more and the world is more connected than ever" angles won't change too dramatically going forward, so I'm skipping them because I think any effect there will be dominated by...
2. What happens to biotechnology / virology over the next century?
i. Of course the default assumption is a background of steadily advancing technical capability.
ii. Will academic gain-of-function research, or research on dangerous pathogens in general, increase or decrease in the future? (Hopefully decrease, as Covid-19 was plausibly the result of research like this!) Will containment/security around this research improve?
iii. Will malicious bioterrorism / biowarfare attempts become more likely? (Sadly I suspect so, even more than would be expected from generally advancing technology over time, since Covid-19 has raised the salience of pandemics for so many people.)
B. Going forwards, what is the likelihood that we respond competently to stop a newly-arisen pandemic early?
1. How much do we improve early detection (genetic sampling, worldwide health infrastructure, etc)?
2. How well are we likely to do at early containment via distancing, contact tracing, lockdowns, etc? (Such as how we shut down classic SARS)
3. This doesn't count as much since it's not as early, but how well do we roll out late-game responses like rapid mass-scale vaccine development?
Personally, I am pessimistic about new pandemics -- even if the whole world takes a hard line against irresponsibly dangerous virology research (hard to do when the US and China don't even seem interested in a fair investigation!), it's still swimming upstream against a tide of increasing technical capabilities in biotech as a whole. And then you've got malicious actors to worry about! But I am optimistic that there is a bunch of good stuff to do in terms of building quick-response capability, and also optimistic that some of that stuff will actually probably happen. The answer to your question is the outcome of a race between those two factors.