Try overrding your model get_report_values function and pass to it a variable containing current user (Employee) object and use it in your template (<span t-esc="employee.department_id.name"/>)

@api.model
def get_report_values(self, docids, data=None):    
    docs = self.env['your.model'].browse(docids)    
    employee = self.env['hr.employee'].search(['user_id', '=', self.env.user.id], limit=1)    
    return {        
        'doc_ids': docids,        
        'doc_model': 'your.model',        
        'docs': docs,        
        'employee': employee and employee[0]    
}

In res.partner "department_id" not available, you can create one compute field in res.partner which is set department of that partner.

from odoo import fields,models,api
class res_partner(models.Model):
    _inherit='res.partner'
    @api.multi
    def set_department(self):
        user=self.env.user
        for record in self:
            employee_id=self.env['hr.employee'].search([('user_id','=',user.id)])
            record.department_id=employee_id and employee_id.department_id.id or False
department_id=fields.Many2one('hr.department',compute='set_department',string="Department")

After creating compute field ,your code will be work.