Hi Girl Guide,
It's Clara Jane Martin born 19/07/1919 Swatragh, Derry, Northern Ireland born to Clara Jane Martin and Robert Martin. The mothers maiden name was Turner.
We need the birth certificate to get a passport. As its not 2019, it wont be online, I am not sure on who to contact to order it.

Hi,
You have enough info about Clara to order(submit the application) online.
https://www.nidirect.gov.uk/articles/ordering-life-event-certificates. On the online application ,fill in all the steps - add words to the steps if you are not 100% sure of your info . For instance if you're not 100% sure of where the birth took place , in the birth box you could say "Swatragh, Derry ,
I think" The above link also gives their phone number if you do want to order over the phone ( you pay extra for priority mail 20 pounds opposed to the usual 15 pounds)
I ordered online from Groni a 1918 and a 1940's one with a little less info than you have and I used the words I think (these were also for passport reasons) and had no problems, They sent out both the certs to me. There is a box there for "Additional information to support your application " fill that in with any extra details such as "this is my grandmother /mother " , we need the cert for passport reasons etc, etc . As long as you fill out all the boxes (even with the words "I think") and give as much info as you possibly can and know, you should not have any problems.
Also, for passport reasons, I doubt that the view online ones would be any help to you for passport applications even if yours was over 100 yrs old. Passport applications usually need the hard copy certified certs and not screen grabs or copies ,unless a hard copy is signed by a justice of peace. (You can't download certified certs from them , most people screen grab them). They are no good for official purposes such as passport applications
Kind Regards