I think, in this case, what you need to do is link the table into each of the client applications and append records to it.
This works best if the shared table is in another Access database, other types of table might work, such as .dbf files or Exxcel spreadsheets, but there might be sharing violations with multiple links into non-Access files (some of this will also be determined by the file locking characteristics of your network)
HTH
Mike