The Scotland midfielder left Brighton for the Azzurri in August and admits he's happy playing for coach Antonio Conte.
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Gilmour told BBC Sport: "If there is a problem, he tells you and tries to solve it. I am really happy to work with him."
Gilmour then explained his decision to join Napoli: "I wanted to push myself further, to see how far I could go. I have to thank Brighton, they were very good with me, they helped me a lot.
"But I have no regrets, I know I made the right choice and I'm very happy to wear the blue shirt. I hope to do well in Naples and to get some great satisfaction with my teammates."