edite.blade.php

@extends('admin.layouts.app_admin')

@section('content')
    <div class="container">

        @component('admin.components.breadcrumb')
            @slot('title') Редактирование сотрудника @endslot
            @slot('parent') Список сотрудников @endslot
            @slot('active') Редактирование @endslot
        @endcomponent

        <form class="form-horizontal" action="{{route('admin.employee.update', $employee)}}" method="post">
            @method('PUT')
            @csrf

            {{-- Form include --}}
            @include('admin.employee.partials.form')
        </form>
    </div>
@endsection

Employee

namespace App;

use Illuminate\Database\Eloquent\Model;

class Employee extends Model
{
    // Mass assigned
    protected $fillable = [
        'last_name',
        'first_name',
        'middle_name',
        'gender',
        'birthdate',
        'telephone',
        'mobile',
        'ip_telephone',
        'email',
        'departament_id',
        'position_id'
    ];
}

EmployeeController

    public function update(Request $request, Employee $employee)
    {
        $employee->update($request->all());

        return redirect()->route('admin.employee.index');
    }
    
    Состав $request следующий:
          array(12) {
  ["_method"]=>
  string(3) "PUT"
  ["_token"]=>
  string(40) "GH19wQ7k98aKld1PUkx5jZVXO5v7lFbWHeKR5FwF"
  ["last_name"]=>
  string(12) "Иванов"
  ["first_name"]=>
  string(18) "Иван"
  ["middle_name"]=>
  string(20) "Иванович"
  ["birthdate"]=>
  string(10) "2018-12-31"
  ["telephone"]=>
  NULL
  ["ip_telephone"]=>
  NULL
  ["mobile"]=>
  NULL
  ["email"]=>
  NULL
  ["departamen_id"]=>
  string(1) "1"
  ["position_id"]=>
  string(1) "1"
}

form.blade.php

<div class="container">
    <div class="row">
        <div class="col-sm">
            <div class="form-group">
                <label for="departamen_id">Отдел</label>
                <select id="departamen_id" name="departamen_id" class="form-control form-control-sm">
                    @if(isset($employee->departament_id))
                        @include('admin.employee.partials.departament', ['departaments' => $departaments, 'departament_id' => $employee->departament_id])
                    @else
                        <option value="" selected="selected"></option>
                        @include('admin.employee.partials.departament', ['departaments' => $departaments])
                    @endif
                </select>
            </div>
        </div>
        <div class="col-sm">
            <div class="form-group">
                <label for="position_id">Должность</label>
                <select id="position_id" name="position_id" class="form-control form-control-sm">
                    @if(isset($employee->position_id))
                        @include('admin.employee.partials.position', ['positions' => $positions, 'position_id' => $employee->position_id])
                    @else
                        <option value="" selected="selected"></option>
                        @include('admin.employee.partials.position', ['positions' => $positions])
                    @endif
                </select>
            </div>
        </div>
    </div>
</div>