While currently there's no native integration between Pitchbook and HubSpot, if you could share more about your team use case, I'd be happy to suggest some APIs that your team can use i.e. if you're looking to retrieve HubSpot contacts to populate in Pitchbook, you can use the CRM API | Contacts.
The way we would want to use the integration is to pull potential companies that fit what we are looking for. There's a couple of ways the data could integrate to help us:
1) We do a lot of market research and sometimes want to know what research we have done in a deal. It would be great to see which companies we have tapped for market research and their description and details
2) Be able to search pitchbook data through HubSpot - when looking at a company in HubSpot for it to show similar companies and be able to add them to a pipeline instantly
3) Be able to do workflows with pitchbook data - for example, when X company we are tracking gets funding, add them to a pipeline and send a notification to a user.
Having said that, if you haven't already, I'd recommend jumping over to the HubSpot Ideas Forum and posting this idea there so that it's visible to the HubSpot product team and other HubSpot customers and developers. Hopefully this will gather more interest.