The following works in PostgreSQL:

with _data as (
    select
        asp.id submission_portal_id ,
        ea.tax_number,
        ea.id application_id,
        (
            select
                count(1)
            from
                eae_field ef 
            join eae_field_geospatial_data efgd 
                on ef.id = efgd.field_id 
            where
                ea.id = ef.application_id 
        ) field_count,
        (
            select
                count(1)
            from
                eae_livestock el 
            join eae_livestock_stable els
                on el.id = els.livestock_id
            where
                ea.id = el.application_id 
        ) stable_count
    from
        eae_application ea
    left join eae_applicant_commitment eac
        on ea.tax_number = eac.tax_number
    left join app_submission_portal asp
        on eac.submission_portal_id = asp.id
    where
        ea.application_status_id in (2) and
        asp.id = 569
)
select
    *
from
    _data t
where
    t.field_count > 10 and
    t.stable_count > 3
;