The phrase "to refresh the drink" means to fill up or replenish a drink that is empty or nearly empty.
Sentences with «to refresh the drink»
You can look forward to gourmet meals and refreshing drinks at their onsite restaurants, and may be able to book relaxing massages or beauty treatments at the hotel's own spa. (anywhere.com)
There is also a swim - up bar located at the center of the lagoon where guests can enjoy refreshing drinks without leaving the pool. (philippinestravelpackage.com)