personally I'd leave it and pot up into a slightly bigger pot come spring just as they start into new growth. They do better in a soil based compost rather than a peat based one.

Believe me the agapanthus loves to be totally pot bound.
The best ever agapanthus I grew lived in a pot for years and every year produced 16 (or there abouts) beautiful flower heads. One morning I got up and the plant had burst the pot and looking at the root system there was no soil there at all. I have grown them for 20 years. They are very frost hardy and I just move the pots close to the wall of the house....other than that they are out all winter. If you like a deep blue agapanthus a real beauty is Northern Star .... it is a wonderful plant. Water well in summer and I do feed mine too in summer...other than that just let them get on with it.

Thank you for asking the question. I have never had any luck trying to grow these but i have potted some up this year and will not now transplant in to the garden. Can I plant the pot - black polythene plant pot - in the ground so that it looks as if it is growing in the border and will that suffice to keep it frost free over the winter or will I have to bring them in to the greenhouse ?

Thanks everyone. In answer to the question that I was asked, apparently they are quite frost hardy, but it is recommended that the pot is moved next to the wall of the house at least over winter.