There isn't a
fa fa-search
element in your code.
Assuming you want it to be part of the same input group as the button, you just need to add it with the correct class:
<div class="form-group row">
<div class="input-group col-md-4">
<div class="input-group-prepend">
<span class="fa fa-search" aria-hidden="true"></span>
</div>
<input class="form-control py-2 border-right-0 border" type="search" value="search" id="example-search-input">
<div class="input-group-append">
<button class="btn btn-outline-secondary border-left-0 border" type="button">
</button>
</div>
</div>
</div>
Input group · Bootstrap v4.5[
^]
Also, stop using the
<center>
tag. It has been obsolete for over 20 years now.