Tapestry weavers who make works large or small can enter upcoming juried exhibitions. You just need to send images of your work, within any parameters set, and hope the jury prefers it to others submitted. Sometimes a fee is also required, and you usually have to pay for the shipping in both directions. In Europe there are quite a few shows for textile artists to try for. Here are three coming up:

16th Lodz Triennial ‘Breaching Borders’ – deadline 18 January 2019 (extended from November 2018). No fees required. This show used to be invitational only, but for the first time it is open call. Exhibition 5 October 2019 – 15 March 2020.

16th International Triennial of Tapestry in Lodz 2019

Garden of Eden – deadline 15 February 2019. The show will be held in Haslach, Austria, 17 July – 4 August 2019. No fees required. It will be supplemented by a conference run by the European Tapestry Network.
https://www.gardenofeden2019.org/en/details-1451/garden-of-eden-group-exhibition-with-open-call

‘Pop-Up’ – deadline 31 March 2019. This is a show of miniature three-dimensional textiles held in Como, Italy. Maximum size is 20 x 20 x 20 cm. It is organised by Arte & Arte and held 28 September – 17 November 2019, after which it tours internationally. Fee 30 euros.
https://www.miniartextil.it/en/edition-2019/

Best of luck!

Garden of Eden