Obtaining TESS input catalog (TIC) IDs for Gaia `source_ids`?
You can query TIC by Gaia ID. Using the MAST Portal, MAST Catalogs, TESS Input v7, Advanced Search form, I specified:

GAIA ID: 4052922352453886976

and got a single result:

TIC ID (ID):            50559830
RA (ra):                275.945292 (18:23:46.870)
Dec (dec):              -25.672353 (-25:40:20.47)
TESS Mag. (Tmag):       13.579
Version (version):      20180610
UCAC ID (UCAC):         322-168973
2MASS ID (TWOMASS):     18234686-2540204
GAIA ID (GAIA):         4052922352453886976
GAIA G Mag. (GAIAmag):  14.5068


Since the MAST portal currently provides TICv7, the Gaia ID is probably from Gaia DR1.
The TIC release notes say Gaia DR2 data are new in TICv8.


  9&nbsp;&nbsp;GAIA&nbsp;&nbsp;The matched Gaia DR2 identifier has been updated in TICv8.
  Gaia IDs in TICv8 are included for stars that are found in the Gaia-provided Gaia-2MASS look-up table.
  These identifiers have been updated by the Gaia team from DR1 to DR2, and may not be consistent between TICv7 and TICv8.