The governing body was left short at the top with the departure earlier this year of player director Steven Martens, who returned to his homeland to take up a role with the Belgian Football Association.
Head of women's tennis Nigel Sears then resigned during Wimbledon after being offered the position of coaching former world number one Ana Ivanovic, leaving only head of men's tennis and Davis Cup captain Leon Smith in a senior performance role.
After five years in his position, Draper has turned his focus from recruiting high-profile names such as Paul Annacone and Peter Lundgren to giving opportunities to young British coaches, and he does not foresee major changes.
Draper said: "We spent a large part of July and early August talking to a lot of the players and coaches to see where we are.
"We've been trying to keep a lot of the team who are in place locked in for three to five years, because we always said this is a 10-year journey.
"We have got some great coaches on board, and some really good young British coaches as well. Leon's done fantastically well on the men's side.
"We're not that far away now. We're looking at strengthening the team again over the next few weeks. For us it's the balance of continuity with bringing some fresh blood in.
"I think we've got a good coaching set-up not just within the LTA but across British tennis now."
Draper has been heavily criticised for British tennis' poor showing at the top of the game, Andy Murray aside, over recent years but this season has provided some encouraging signs.
The women's game has continued its gradual improvement, with four women in the main draw at the recent US Open, while three out of the four semi-finalists in the boys' singles at Flushing Meadows were British, with Oli Golding going on to lift the trophy.
Draper believes that progress can be seen throughout the age groups, and he said: "Overall we've had a pretty good summer on the performance side of things.
"We've always known it's about getting the depth through in the juniors and it's nice now because I think the rest of the world have been taking note that the British players are coming in the junior ranks. It's not just a one-off.
"In European and world terms we're certainly getting the standards up to the level we expect. But we know this is just the starting line and there's a hell of a lot of hard work to do now."
Draper was talking at the opening of five new public courts in Brodie Park, Paisley, which will be free to use.
There will also be free coaching in a partnership with charity Tennis For Free, who have been critical of the LTA for not doing enough to change the elitist image of the sport.
The governing body has focused increasingly on the grass roots, and Draper added: "A big part of our job is to grow the sport and get more people playing.
"Obviously it helps the better the top players are because that helps increase interest in the sport but it's really about getting people coming to facilities like this and having a good time."