I am under the impression that you may apply for EI immediately upon retirement, the problem being that if you do at that time your pension will be considered as income and will be deducted from your EI. If you re qualify at a different job your pension may not be considered as income and may not be deducted. As per the service Canada website.
All I actually know for sure is that when I retired I was informed by EI that my pension was more then I would receive from them thus having a net value of 0, although I could apply if I wanted to. After I had re qualified I was then able to collect EI during my annuitant break. And being an evil double dipper I did. >
"Pension income resulting from any employment constitutes earnings for benefit purposes. These include:
Employer pension plans, including employment as a member of the Armed Forces or any police force. This also applies to pensions from employment in another country, whether or not the employment was insurable.
The Canada Pension Plan
The Quebec Pension Plan
Pensions income resulting indirectly from employment do not always constitute earnings. In the following cases, all or part of the pension is not considered to be earnings:
The pension of an individual who re qualifies for EI benefits after the date on which payment of the pension begins.
Disability pensions from employment as well as disability pensions from the Canada Pension Plan or Quebec Pension Plan"