burning, deep, fervent, fierce, great, intense, passionate, strong, urgent
growing
There's a growing desire among consumers for more organic products.

sudden
insatiable, unquenchable
Most children have an insatiable desire for knowledge.

overwhelming, uncontrollable
frustrated, thwarted, unfulfilled
repressed
hidden, secret
She confessed a secret desire to be famous.

earnest, genuine, real, sincere
selfish
desperate
obsessive
human
The human desire for answers is very great.

individual, personal
innate, natural
subconscious, unconscious
basic
The search for a better life is one of the most basic desires of human beings.

conflicting
He is filled with conflicting desires.

carnal, erotic, sexual
heterosexual, homosexual, same-sex
mutual
a long-lasting relationship based on our mutual desire for peace

feel, harbour/harbor, have
I suddenly felt an overwhelming desire to laugh

share
He did not share her desire for books.

arouse, create
His childhood had created a desire for stability in his life.

fuel, stimulate
This was all Liam needed to fuel his desire for revenge.

articulate, communicate, express, indicate, profess, reveal, signal, state, voice
The chairman expressed his desire to expand the company.

fulfil/fulfill, gratify, indulge, satisfy
control, overcome, resist, suppress
He suppressed the desire to run from the room.

demonstrate, reflect
His actions reflect his desire to fit in.

be driven by, be motivated by
They were motivated by a deep desire for money and fame.

desire for
Horses need to satisfy their desire for space and freedom.

an object of desire
He felt he was nothing more to her than an object of desire.

greatly, really, truly, very much
A home of her own was something she had always very much desired.

Desire is used with these nouns as the subject:
heart