David Houlgate, branch secretary at Unison Harrogate, said "the strain is starting to show" on staff under pressure from heavier workloads after the council introduced a temporary halt on hiring in May last year and shrunk its workforce by almost 60 jobs.
"If you were to liken the situation to an elastic band, you can keep stretching it but eventually it will snap," Mr Houlgate said.
"We know that some staff are finding the ongoing situation difficult and mental health and wellbeing is an increasing concern for us.
"The council has put in place help and assistance procedures which are welcome but this is not always enough. The pressures are still there and staff are still leaving."
A spokesman for Harrogate Borough Council said no end date had been agreed for the recruitment freeze which was introduced to keep costs down during the Covid-19 outbreak.
The pandemic is expected to cost the council another £5.9million this year and although it is forecasting a balanced budget, councillors had raised concerns that the strain of balancing the books will be placed on staff.
In its spending plans for 2021/22, the council has set aside funds for the jobs affected by the recruitment freeze. Mr Houlgate said while this was welcome, the halt on hiring should "end now".
"It is clear to us that the strain is starting to show with staff who are now facing the perfect storm," he said.
"They are having to deliver the usual vital council services but also the additional help and support in relation to the pandemic. They are having to do so whilst in many cases working in isolation now for almost a year whilst working during a recruitment freeze.
"Anything that can alleviate the situation, such as a return to normal recruitment procedure, would be helpful but it may not be enough. So we urge the council not to delay."
Harrogate Borough Council had 1,117 members of staff at the end of March 2020 - a figure which has now been reduced to 1,061.
The authority said it had avoided putting any staff on furlough by redeploying workers in lockdown-hit services into different roles. This, for example, has included leisure centre staff being moved into waste collection teams.
Mr Houlgate said the response from staff had "phenomenal" and that it was also "good news" that the council is in a better financial position than it was last year when it was forecasting a £10.6million shortfall as a result of the pandemic.
He added: "Whilst the council is not in a great financial position due to the pandemic and is having to use some of its vast reserves, the situation does look much better than it did a few months ago. This is good news.
"It must be remembered also that local government has been a victim of chronic underfunding by central government now for over 10 years and that even before the pandemic there were huge job cuts leading to increased workloads."
A council spokesperson said: "The recruitment freeze was introduced in May 2020 as part of our Covid-19 recovery plan and so that staff from other services could be redeployed.
"This recruitment freeze does not apply to business critical posts that cannot be fulfilled by redeployment. An end date hasn’t been decided."
By Jacob Webster, Local Democracy Reporter