Formula to pull data from one sheet to another where multiple values match

Since you are using Excel 2013, Power Query is available for you to download from the Excel Site. Using PQ, I loaded each table to it and then Close and Loaded to a Connection. Then, I merged the two tables with a Left Inner Join on the Identifier and Date. The results were:

Excel 2016 (Windows) 32 bit

	A	B	C	D	E	F	G	H
1	Idenitifier	Forename	Surname	Date	Basic Rate	Holiday Pay	Basic earnings total	paid pension at %
2	603624	Pete	Smith	6/1/2020	700	800	1500	5.8
3	603625	Pete	Smith	4/1/2020	600	200	800	5.6
4	603626	Pete	Smith	2/1/2020	450	200	650	5.6
5	603627	Pete	Smith	12/1/2019	800	200	1000	5.3

Sheet: Sheet2

Review PQ
In the attached file
Click on any cell in the new table
On the Data Tab, click on Queries & Connections
In the right window, double click to open Query
Review PQ steps

M-code basics:
- "let" is the start of a query
- "in" is the closing of a query
- each transformation step sits in between those 2 lines
- each step line is ended by a comma, except the last one
- "Source" is always the first step (Source Data)
- After "in" you have the last step referenced

File attached

The Mcode that resulted from my steps is as follows.

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Do you have MS Access installed on your computer? Have you considered asking your IT department to add Power Query to your machine. It is part of Excel and not some "foreign" software.