Use File... Get External Data... Link to link to the existing tables;
create your new tables, empty, perhaps by using File... Get External
Data... Import and selecting the option to import the design only.

Then run Append queries to selectively append the desired records. If
you Append to an autonumber field, the value will be copied
faithfully, and will not autoincrement; the next autonumber when you
add a new record will be one more than the largest imported number
(though its exact value should not be of importance other than that it
is unique).

                 John W. Vinson[MVP]    

If you are talking about using an autonumber in the new database just create
your table structure including autonumber field.  Paste Append the record
including the number field.
This will work so long as your do not have a duplicate number.  
But where do you plan to go from there?  Continue to copy and append?  
Are will you start add new records standalone in the new database?