The C7sus4(13), or better just Csus13 respectively C13sus, is a 7sus4 chord with an additional 6th (A). The 6th has to be notated as 13 in the chord symbol (as if you would count up to the same note an octave higher), because it supplements the 7th instead of replacing it (6th chords like C6 have NO 7th!).
You are free to play a 9th (D) in the Csus13 chord as well. It does not have to be written in the chord symbol like C7sus4(9,13) or Csus(9,13).
The Csus13 has the tones C (1), F (4), G (5), Bb (7), A (5) and optionally (but very common): D (9)
The 5th is usually omitted.
If you play the Csus13 with the 9 and omit the 5th, you can see it as Bbmaj7/C slash chord (Bbmaj7 chord with C as bass note). That notation even better represents the chords sound.
Especially if you play the chord with the 9 and without the 5th (Bbmaj7/C), the Csus13 has a special character that reminds of a horn section. Furthermore you can move that chord around quite freely. For example for an intro in whitch each chord is played one or more bars like e.g. Gsus13 Bbsus13 Dbsus13 Csus13 respectively Fmaj7/G Abmaj7/Bb Bmaj7/C# Dmaj7/E in slash chord notation.
These maj7 chords can also be seen as maj9 chords, since the bass notes are their 9ths. Voila! Maj9 chords sound great as well, when moved around freely!
Of course the Csus13 can be played as a replacement for a C7 (as described for the sus9 chord).