You have 2 choices. You can do it discretely; after work hours, no the may not contact my employer. Or, you can do it openly; multi-hour lunch breaks, lots of personal time off, and your LinkedIn profile is super active.

The latter will either get you a salary increase or you'll be shown the door. Ask me how I know.

I haven't had an on-site yet that didn't require blocking off an entire day.

I have had half-days (my company does that too) which pretty much require a full day off.

I guess it helps to work remote a lot. Much easier to disappear for a while.