An additional floor at 140 West George Street in the city has been leased which means the firm is now based across three levels in the office block.
A move to a larger site in Edinburgh took place in August this year with the firm suggesting it is keen to hire additional lawyers in areas including financial services, leisure and renewable energy.
Bristol based TLT moved in to Scotland through a merger with Anderson Fyfe in July last year.
Since then it has grown its staff in Glasgow from 45 to 61. TLT hopes to double the size of the Edinburgh office, where it employs six people, in the coming months.
Tom McEntegart, the head of TLT Scotland, indicated he is expecting the firm to continue doing well going in to 2014.
He said: "We are focused on building further our expertise in the financial services, leisure and energy and renewables sectors.
"We have made some significant hires since the merger; including licensing partner Stephen McGowan and real estate associate Simon Williams.
"In 2014, we expect to grow the firm by 25% as we respond to increasing demand in the market, especially in our chosen sectors."
Prior to the merger TLT derived around 40% of its income from financial services clients while Anderson Fyfe had a specialist niche in recoveries for financial services businesses.
The combination of the two firms was partly driven by large clients looking to use one firm to handle all legal requirements across the UK.
In June this year TLT, which also has offices in Belfast, Manchester and London, said its fee income had grown from £44.5 million to £49m in its 2012/13 financial year. The Anderson Fyfe practice contributed around £2.4m across the 10 months it had been under the TLT banner.