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PipedriveExperts has done just this type of integration for a number of clients, including a complex integration to our own SaaS product (BrokrBindr, which happens to be a tool for mortgage professionals).
If you wish to have the integration be bi-directional, I would recommend that you employ Webhooks. We have done this previously, and I confirm that data changed in either Pipedrive or Klaviyo is immediately reflected in the other product. Typically under 2 seconds. This type of integration requires more effort from a dev team.
The alternative would be a uni-directional integration. For this purpose, a tool like Zapier (or better: Make.com/Integromat) could be a less-expensive option but certain compromises may present themselves.
I invite you to please contact me if we may be of assistance.