The Scottish giants won the race to land the promising midfielder earlier this year and handed him a three-year professional contract to continue his development at Ibrox.
Lindsay was left impressed by a meeting with Steven Gerrard and Thomson is now looking to bring out the best in the midfielder over the coming years.
Rangers have a number of promising youngsters they are looking to push through to the first team and full-back Nathan Patterson was involved against Bayer Leverkusen in midweek.
Thomson insists there are more youngsters where Patterson came from, with a special nod towards Northern Irish talent Lindsay.
“Kai Kennedy’s had a bit of speculation in the papers etc. Josh McPake made his debut last year. Dapo [Mebude] made his debut last year, so there’s certainly other ones [besides Patterson] coming through”, Thomson said on Rangers TV during the Gers’ win over St Mirren.
“We’ve got an Irish boy, Charlie Lindsay, who’s just signed. He’s only 16, but he could be anything.
“Terrific boy, brilliant to work with.”
Lindsay became the youngest player to play for his former club Glentoran when he was brought on against Ballyclare Comrades at the age of 15.
The teenage talent was a identified as a priority for Rangers, with the club pulling out all the stops to secure his signature.