Swansea Council says 800 applicants have applied for its apprenticeship scheme, of which twelve places are on offer.
It comes as a new report predicts 7,000 more people could become unemployed in Wales this year.
The survey by think tank the Institute for Public Policy Research also found that 41,000 extra under 25-year-olds in the UK will be out of work - a new record.
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Her suspension comes after she criticised Mr Hamilton for not supporting a policy on dignity and respect.