Here is a recording from The Guardian podcasts which illustrates how important it is not to pronounce the /h/ phoneme in certain contexts.
Notice that the speaker says ǀwɪl iǀ and not ǀwɪl hiǀ.
Today, Emmanuel Macron has won the presidential election in France, but how will
he try to unite a divided contry (Nosheen Iqbal, The Guardian podcast).
Interesting, isn’t it? However, you’re not allowed to do this whenever you want. There are very precise rules (and they are quite easy to learn).
If you want to know everything there is to know about the elision of the /h/ (and other types of elision), go here: