Trippier largely played second fiddle to Walker at City following his move from Burnley in 2015 but following the latter's £50m move to City in July, Trippier has been cast into the spotlight as first choice.
Despite the promotion, Trippier insists that he was not happy to see Walker leave, saying that the pair enjoyed a good relationship.
The 26-year-old told 'Sky Sports News': "We had a great relationship, me and Walks, obviously there were rumours that he was leaving, but people move on.
"I wasn't [pleased to see him go]. I've known Walks for years, we were really good mates even when we were here together, and whoever we're playing we always tried to encourage each other and help each other. We did that when we were here.
"But Walks has moved on now to Man City, and I just want to do my best to keep the right-back slot my own. Obviously I've worked hard in pre-season, and since I've been at Tottenham to be honest, I've waited patiently.
When asked about how the move impacted him, Trippier stated: "My reaction was that I just need to work even harder, to keep working hard on the training field so when I get the opportunities on the pitch I can do the best to my ability for my team-mates and the club."
"I was delighted that I got the nod to start against Chelsea. I want to work hard in training, and make sure I can keep the shirt."
With rumours of an imminent move for PSG's Serge Aurier, Trippier may have to be at his best to make the right-back berth his own for Mauricio Pochettino's side but he certainly seems to be up for the challenge.