You can get the opportunities from the field client.opportunity_ids. If you want to get all leads, you need to search for them:

# Check if the record has a partner_id
if record.partner_id:
    client = record.partner_id
    # Attempt to find a lead linked to the client
    lead_ids = record.env['crm.lead'].search([('partner_id', '=', client.id)])
    # Check if any leads found
    if lead_ids:
        lead_ids.unlink()

Note that the check if lead ids were found is not necessary and you can directly call unlink on the recordset:

record.env['crm.lead'].search([('partner_id', '=', client.id)]).unlink()

If you do not want to delete the leads, I suggest to archive them:

if lead_ids:
    lead_ids.write({'active': False})