In the article Power Apps: Filter A Gallery With Multiple Dropdowns I mentioned the employee-dropdown could be replaced with a People Picker instead.  Here’s how to do it:

Update the Employee column to Person type in the Paid Time-Off SharePoint list.  Leave all other data the same as before.
| TimeOffDate | Employee | TimeOffType | Status | 
| 9/1/2020 | Kelly Smith | Personal | Submitted | 
| 9/4/2020 | Kelly Smith | Vacation | Approved | 
| 9/5/2020 | Kelly Smith | Vacation | Approved | 
| 9/8/2020 | Jennifer Houston | Vacation | Rejected | 
| 9/12/2020 | Sarah Green | Personal | Submitted | 
| 9/13/2020 | Jennifer Houston | Vacation | Approved | 
| 9/15/2020 | Sarah Green | Personal | Rejected | 
| 9/18/2020 | Kelly Smith | Personal | Rejected | 
| 9/19/2020 | Sarah Green | Sick | Approved | 
| 9/21/2020 | Jennifer Houston | Personal | Submitted | 
Add the Office365Users connector to your app.

Create a ComboBox called cmb_Employee and place it beneath the Type and Status dropdowns.

Write this code in the following properties of cmb_Employee
DisplayFields: ["Display Name"]
SearchFields: ["Display Name"]
Items: Office365Users.SearchUser({searchTerm: Self.SearchText, top: 100})
IsSearchable: true
SelectMultiple: false
Then change the Items property of the Gallery to this code.
Filter(
    'Paid Time Off',
    drp_Type.Selected.Value=Blank() Or TimeOffType=drp_Type.Selected.Value,
    drp_Status.Selected.Value=Blank() Or Status=drp_Status.Selected.Value,
    cmb_Employee.Selected.DisplayName=Blank() Or Employee=cmb_Employee.Selected.DisplayName
)
The people picker will now filter the gallery.

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