I'm on maternity/paternity leave and the department has yet to send my Record of Employment to Service Canada?
You must first contact Service Canada's Employment Insurance Program Section to explain the situation in detail. Service Canada should be in a position to provide instructions on advancing your maternity/paternity claim forward.
Generally, the common rule is to ask questions and explain the predicament to Service Canada beforehand, concerning any difficulties you may be experiencing with the employer. If Service Canada knows a problems exist in advance, it usually will not apply any penalties. A maternity/paternity claim must be filed within 4 weeks from your last day worked.