First and foremost, make a backup copy of the DB before you do anything else that would potentially remove data. Keep it around just in case things go badly.
There are two or three approaches. They depend on how much you want to do with your old data after it is "officially" old.
Method 1: Simply add a Y/N flag to the record that says "Officially Old" (using whatever name seems right for the intent.) Mark the records meeting the criteria. Then when you look at that table intending only to work with current data, include a where clause in the query that says (more or less) "WHERE ... AND ( OFFICIALLY_OLD = FALSE )". As long as you are not approaching 1 Gb table size or 2 Gb total database size, you are good as gold.
Method 2: For size reasons, you want to really get rid of the old records but you might still wish to look at them. As it happens, you can have multiple back-ends linked to the same front-end. SO... you can build your archiving table in a second file that will contain up to 1 GB in this table. Permanently link to this "Archive back-end" from the FE. Then have the same flag noted in my method 1 and use it for two queries: First an "INSERT INTO archiving_table (field-list) SELECT field-list FROM active-table WHERE OFFICIALLY_OLD = TRUE ;" followed by "DELETE * FROM active-table WHERE OFFICIALLY_OLD = TRUE ;".
Once you do this, you need to carefully perform a Compact & Repair before letting this system go active again. Then as suggested, you can query the archiving table separately or in conjunction with a UNION query. The pitfalls in method 1 and 2 BOTH revolve around an Access limit that says no recordset can grow to greater than 1 Gb and no single back-end file can grow to greater than 2 Gb.
Method 3: (Included for completeness purposes) If your dataset is getting that large that you really NEED to do this AND you want to retain the data for running analytics on a regular basis, consider something like an active SQL backend - like SQL Server, MySQL, or any one of a number of other similar products. Then up-convert your Access back end to an active-SQL backend. This might be more than you wanted to do, but to give you a complete list, I felt I should include it.
Method 4: For the case where you will NOT be referencing the old data but would like to keep it around for snorts & giggles. Instead of doing an INSERT INTO for another table, look at exporting the table to an Excel workbook based on a query that selects the obsolete records. DoCmd.OutputTo can take a query and put it out in another format.