Answer: Your agapanthus is a reblooming type which means that after all the flowers on the flowering stalk are spent, you'll need to cut the stem off the plant. In a few weeks a second stalk will emerge and flowering will begin all over again. You can certainly pinch or pull off the spent blooms, one at a time, to keep the plant looking nice, but doing so won't encourage the same stalk to produce more flowers. What triggers reblooming is removal of the old flowering stalk.
Enjoy your new agapanthus!
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