We construct new families of groups with property (T) and infinitely many alternating group quotients. One of those consists of subgroups of
A
u
t
(
F
p
[
x
1
,
…
,
x
n
]
)
\mathrm {Aut}(\mathbf {F}_{p}[x_1, \dots , x_n])
generated by a suitable set of tame automorphisms. Finite quotients are constructed using the natural action of
A
u
t
(
F
p
[
x
1
,
…
,
x
n
]
)
\mathrm {Aut}(\mathbf {F}_{p}[x_1, \dots , x_n])
on the
n
n
-dimensional affine spaces over finite extensions of
F
p
\mathbf {F}_p
. As a consequence, we obtain explicit presentations of Gromov hyperbolic groups with property (T) and infinitely many alternating group quotients. Our construction also yields an explicit infinite family of expander Cayley graphs of degree
4
4
for alternating groups of degree
p
7
−
1
p^7-1
for any odd prime
p
p
.