A verb for “to join” in the Gnomish Lexicon of the 1910s formed with the prefixal form of G. artha- “approach” (GL/20). Its second element might be G. gada- “join, connect, unite” (GL/36).
Gnomish
gada-
verb. to join, connect, unite
arthaid-
verb. to join
A verb appearing as gada- “join, connect, unite” in the Gnomish Lexicon of the 1910s based the early root ᴱ√yat- [ẎATA] (GL/36), with the Gnomish sound change of initial y becoming g.
Neo-Sindarin: The later form of this root is ᴹ√YAT or √YAN, so I would update this verb to ᴺS. ianna- “to join, connect” for purposes of Neo-Sindarin, inspired by the neologism ᴺS. goianna- “join with, add to”. For “unite” I would instead use S ertha-.