"Keep tabs" can be replaced with a variety of other terms depending on the context it's used. For instance, "monitor" is a great replacement when you have to track something consistently. Similarly, you can use "track," "watch," or "follow-up" to convey the idea of continuously observing something. If you want to communicate that you're staying in control or remaining up-to-date, using "keep in check" or "maintain oversight" would be a more fitting synonym. Lastly, you can use "keep an eye on," "be on top of," "stay informed," or "stay attuned" to describe the concept of being knowledgeable about a particular situation or thing.