The Financial Services Union has warned that jobs in the sector could be in jeopardy if there is continued political instability in Northern Ireland.
The warning comes days after First Trust Bank announced it was closing half its branches in Northern Ireland.
The organisation's general secretary Larry Broderick told the BBC's Inside Business programme that other EU countries were lobbying to take jobs out of the UK ahead of Brexit.
"Unless we in Northern Ireland get together and have a strategy, first of all to copper-fasten the jobs we have and to bring reassurance, but also it's a very competitive environment in Northern Ireland," he said.
"So I think work has to be done and in the absence of political stability and a direction and a plan in relation to that, we think in our sector, certainly there will be a lot of vulnerability of the jobs that are there as well."
First Trust Bank announced on Wednesday that as many as 130 jobs will be lost with the closure of half its branches later this year.
The bank, which is owned by Dublin-based AIB, is one of the so-called "big four" banks in Northern Ireland.