Hi! Good question...
- According to classical and traditional theory, you should incluye all 4 notes of the tetrad (4-note chord) before adding tensions (9, 11, #11, b13, 13).
For example, if you need to use the 9 tension in a C major chord, you should include:
All 4 notes of the tetrad: C (Root), E (Major 3rd), G (Perfect Fifth) and B (Major Seventh)... then D (9th)
... and the chord would be spelled as Cmaj7(9)
- In contemporary harmony/songwriting, you can add tensions to the TRIADS (3-note chords) without adding the 7th.
For example, you can have a chord consisting in just C (Root), E (Major 3rd), G (Perfect Fifth) ... then D (9th)... NO SEVENTH NEEDED!
... and the chord would be spelled as C(add9)
Have you heard The Police? Most of their chords are TRIADS with tension notes (no sevenths).
I hope this is useful for you!
Have a great week